Are the prey- and ratio-dependent functional responses really extremes along a continuum of predator interference?

Transcription

1 Are the prey- and ratio-dependent functional responses really extremes along a continuum of predator interference? f (N) f (N/P) Christopher X Jon Jensen Stony Brook University

2 What is Predator Interference? Reduction in the per capita consumption rate as predator abundance increases Potential mechanisms: Time lost bumping into and handling other predators Resource sharing over longer intervals of feeding reduces overall consumption rate

3 Holling Type II: Per Capita Consumption Rate of Predators Prey Abundance

4 Holling Type II: Per Capita Consumption Rate of Predators Predator Abundance

5 Predator Interference is Real (Salt 1974)

6 Competing Functional Responses f (N) Holling Type II prey dependent increasing predator interference f (N/P) Arditi-Ginzburg ratio dependent Where N is prey density and P is predator density

7 Competing Functional Responses f (N) Holling Type II prey dependent f (N/P m ) Hassell-Varley-Holling predator dependent f (N/P) Arditi-Ginzburg ratio dependent Where N is prey density and P is predator density

8 Competing Functional Responses f (N,iP) f (N) Holling Type II prey dependent Beddington-DeAngelis predator dependent f (N/P m ) Hassell-Varley-Holling predator dependent f (N/P) Arditi-Ginzburg ratio dependent Where N is prey density and P is predator density

9 Does it matter which form of predator interference is used?

10 Does it matter which form of predator interference is used? f (N/P m ) y-holling Functional Response for constant prey, increasing predator at various interfe Instantaneous consumption rate Number of Predators

11 Does it matter which form of predator interference is used? f (N/P m ) f (N,iP) y-holling Functional Response for constant prey, Beddington-DeAngelis increasing predator at Functional various interfe Response for constant prey, increasing predat Instantaneous consumption rate Number of Predators Instantaneous consumption rate Number of Predators

12 Stability Properties of the Extreme Models: Change in Parameter a (searching efficiency) K (carrying capacity) r (prey growth rate) d (pred. death rate) e (conversion eff.) h (handling time) Prey-Dependent Outcome Prey Extinction Prey Extinction no change* Prey Persistence Prey Extinction Prey Persistence Ratio-Dependent Outcome Prey Extinction no change Prey Persistence Prey Persistence Prey Extinction Prey Persistence

13 The Simulations: 1. Numerical approximations of differential equations using Populus Software 2. Designed to mimic behaviors of Didinium- Paramecium system (parameter values from Harrison 1995) 3. Qualitative outcomes explored over a range of r/k values (as planned for my experiments) 4. Parameters r and K linked 5. Non-deterministic criterion for extinction employed

14 m Hassell-Varley-Holling: f (N/P )

15 Beddington-DeAngelis: f (N, ip)

16 Beddington-DeAngelis: f (N, ip)

17 Competing Functional Responses f (N,iP) f (N) Holling Type II prey dependent Beddington-DeAngelis predator dependent f (N/P m ) Hassell-Varley-Holling predator dependent f (N/P) Arditi-Ginzburg ratio dependent Where N is prey density and P is predator density

18 Competing Functional Responses f (N,iP) f (N) Holling Type II prey dependent Beddington-DeAngelis predator dependent f (N/P m ) Hassell-Varley-Holling predator dependent f (N/P) Arditi-Ginzburg ratio dependent Where N is prey density and P is predator density

19 Competing Functional Responses f (N,iP) f (N) Holling Type II prey dependent Beddington-DeAngelis predator dependent f (N/P m ) Hassell-Varley-Holling predator dependent f (N/P) Arditi-Ginzburg ratio dependent Where N is prey density and P is predator density

20 The Paramecium-Didinium system: Paramecium caudatum Didinium nasutum Meets major assumptions of simple predator-prey models: Closed system Can be maintained without heterogeneities/refugia Single prey/single obligate predator Prey food can be delivered as semi-continuous input

21 Answers via Experiment: What is the magnitude of predator interference? Direct measurement of consumption rate over a range of predator densities Curve fitting to HVH and BD models Which model should be used? Microcosm experiments designed to explore the r/k continuum Detection of characteristic extinction events: low r, high K

22 Acknowledgements: Significant contributions to this work have been made by my committee members: Lev Ginzburg, Rob Armstrong, and Dan Dykhuizen I am fortunate to be supported by a National Science Foundation Graduate Research Fellowship and the L. B. Slobodkin Endowment Fund for Graduate Research

23 Non-deterministic Predator Extinction

24 Non-deterministic Dual Extinction

25 Non-deterministic Extinction Criterion: P and N values represent densities of prey per volume In a finite system, a fraction of an individual cannot exist. Threshold extinction density is 1 individual per system Threshold extinction as individuals per volume: Individuals Volume Individuals = System System Volume